Monte Carlo study of a compressible Ising antiferromagnet on a triangular lattice (original) (raw)
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Phase diagram and structural properties for a compressible Ising ferromagnet at constant volume
Physical Review B, 2004
We investigate a model for Ising binary alloys driven by elastic interactions for the case of ferromagnetic interactions and constant volume conditions. The two alloy species are Si and Ge, interacting via the Stillinger-Weber potential, and classical Monte Carlo simulations in the semi-grand-canonical ensemble are utilized in the framework of a compressible Ising model. The volume is selected to be much closer to pure Ge than to Si to provide a significant difference between the species. We find a closed first-order line that divides an "ordered" phase from the disordered state for all temperatures and chemical potentials, in disagreement with theoretical predictions. Visualizations were made to elucidate the surprising structure of the ordered phasewhere the less favorable species (Si in this case) congregates in planes. An interpretation of this equilibrium structure in terms of minimal variations of interatomic distances and angles with respect to the pure phases is made.
2018
We study phase transitions and thermodynamic properties in the two-dimensional antiferromagnetic Ising model with next-nearest-neighbor interaction on a Kagome lattice by Monte Carlo simulations. A histogram data analysis shows that a second order transition occurs in the model. From the analysis of obtained data, we can assume that next-nearest-neighbor ferromagnetic interactions in two-dimensional antiferromagnetic Ising model on a Kagome lattice excite the occurrence of a second order transition and unusual behavior of thermodynamic properties on the temperature dependence.
Phase transitions in the frustrated Ising model on the square lattice
Physical Review B, 2013
We consider the thermal phase transition from a paramagnetic to stripe-antiferromagnetic phase in the frustrated two-dimensional square-lattice Ising model with competing interactions J1 < 0 (nearest neighbor, ferromagnetic) and J2 > 0 (second neighbor, antiferromagnetic). The striped phase breaks a Z4 symmetry and is stabilized at low temperatures for g = J2/|J1| > 1/2. Despite the simplicity of the model, it has proved difficult to precisely determine the order and the universality class of the phase transitions. This was done convincingly only recently by Jin et al. [PRL 108, 045702 (2012)]. Here, we further elucidate the nature of these transitions and their anomalies by employing a combination of cluster mean-field theory, Monte Carlo simulations, and transfer-matrix calculations. The J1-J2 model has a line of very weak first-order phase transitions in the whole region 1/2 < g < g * , where g * = 0.67 ± 0.01. Thereafter, the transitions from g = g * to g → ∞ are continuous and can be fully mapped, using universality arguments, to the critical line of the well known Ashkin-Teller model from its 4-state Potts point to the decoupled Ising limit. We also comment on the pseudo-first-order behavior at the Potts point and its neighborhood in the Ashkin-Teller model on finite lattices, which in turn leads to the appearance of similar effects in the vicinity of the multicritical point g * in the J1-J2 model. The continuous transitions near g * can therefore be mistaken to be first-order transitions, and this realization was the key to understanding the paramagnetic-striped transition for the full range of g > 1/2. Most of our results are based on Monte Carlo calculations, while the cluster mean-field and transfer-matrix results provide useful methodological benchmarks for weakly first-order behaviors and Ashkin-Teller criticality.
Influence of the Pair Correlations on the Phase Transition in an Ising Lattice
Physical Review
We propose a method to incorporate pair correlations of an Ising lattice system in molecular field theory to higher orders. The theory is applied to ferromagnetism, where a system of equations is obtained for the response function (here the susceptibility). We obtain important corrections on the Weiss model and the spherical model. This is illustrated by an explicit calculation of the critical temperature and the spurious phase, appearing for T > T., near the critical point in the case of a simple cubic lattice.
Critical behavior of an elastic Ising antiferromagnet at constant pressure
Physical Review B, 2005
We perform Monte Carlo simulations of a model for a binary alloy exhibiting superstructure formation with two sublattices, in the constant-pressure semi-grand canonical ensemble. This corresponds to an elastic antiferromagnetic Ising model, where spins sit on a distortable diamond net and the interaction is described by the Stillinger-Weber potential. We find a phase transition line separating the disordered from the ordered phase. The finite-size scaling analysis of the critical behavior shows no deviations from three-dimensional Ising behavior. This would be expected in the rigid limit of the model, while for the compressible case, as realized by our model, theory predicts a weak first-order transition.
Analysis of the phase transition for the Ising model on the frustrated square lattice
Physical Review B, 2011
We analyze the phase transition of the frustrated J1-J2 Ising model with antiferromagnetic nearestand strong next-nearest neighbor interactions on the square lattice. Using extensive Monte Carlo simulations we show that the nature of the phase transition for 1/2 < J2/J1 1 is not of the weakly universal type-as commonly believed-but we conclude from the clearly doubly peaked structure of the energy histograms that the transition is of weak first order. Motivated by these results, we analyze the phase transitions via field-theoretic methods; i.e., we calculate the central charge of the underlying field theory via transfer-matrix techniques and present, furthermore, a field-theoretic discussion on the phase-transition behavior of the model. Starting from the conformally invariant fixed point of two decoupled critical Ising models (J1 = 0), we calculate the effect of the nearest neighbor coupling term perturbatively using operator product expansions. As an effective action we obtain the Ashkin-Teller model.
Critical scaling of the mutual information in two-dimensional disordered Ising models
Journal of Statistical Mechanics: Theory and Experiment, 2018
Rényi Mutual information (RMI), computed from second Rényi entropies, can identify classical phase transitions from their finite-size scaling at the critical points. We apply this technique to examine the presence or absence of finite temperature phase transitions in various two-dimensional models on a square lattice, which are extensions of the conventional Ising model by adding a quenched disorder. When the quenched disorder causes the nearest neighbor bonds to be both ferromagnetic and antiferromagnetic, (a) a spin glass phase exists only at zero temperature, and (b) a ferromagnetic phase exists at a finite temperature when the antiferromagnetic bond distributions are sufficiently dilute. Furthermore, finite temperature paramagnetic-ferromagnetic transitions can also occur when the disordered bonds involve only ferromagnetic couplings of random strengths. In our numerical simulations, the "zero temperature only" phase transitions are identified when there is no consistent finite-size scaling of the RMI curves, while for finite temperature critical points, the curves can identify the critical temperature Tc by their crossings at Tc and 2 Tc.
Physical review. B, Condensed matter, 1993
Critical properties of the Ising model on a stacked triangular lattice, with antiferromagnetic first and second-neighbor in-plane interactions, are studied by extensive histogram Monte Carlo simulations. The results, in conjunction with the recently determined phase diagram, strongly suggest that the transition from the period-3 ordered state to the paramagnetic phase remains in the xy universality class. This conclusion is in contrast with a previous suggestion of mean-field tricritical behavior.
Multiple-histogram Monte Carlo study of the Ising antiferromagnet on a stacked triangular lattice
Physical Review B, 1993
The nearest neighbor Ising antiferromagnet on a stacked triangular lattice is a frustrated cooperative system in which it is known that at least two long-range ordered states exist at low temperature. This model has also been of considerable interest as it is known to be a reasonable description of two antiferromagnetic insulators, CsCoBrs and CsCoC13. It has also been the subject of previous theoretical and simulation studies which have yielded con8icting results for the critical phenomena displayed near the transition from the paramagnetic to the high-temperature ordered phase. We have carried out a detailed Monte Carlo study of this system using the recently developed multiplehistogram technique and finite-size scaling analysis, with the purpose of extracting estimates for the critical exponents relevant to this continuous transition. Our results give P = 0.311(4), p = 1.43(3), o. =-0.05(3), and v = 0.685(3) which are not in agreement with previous Monte Carlo work. In addition, although they are close to the expectations from previous symmetry arguments, there are systematic differences between our results and these theoretical predictions. A possible interpretation of these Monte Carlo exponent estimates is that they do not correspond to those calculated for any known universality class, and add to the growing number of simple models of interacting spins, in which geometrical frustration is relevant, which appear to exhibit novel critical behavior. Finally, we have examined the evolution of real-space spin configurations and have seen that a buildup of correlations between anti-phase-domain walls, or solitons, along the stacking direction precedes the transition, an observation which is consistent with recent neutron-scattering measurements on CsCoBr3.